Factorization of fuzzy preferences

In the ordinary framework, the factorization of a weak preference relation into a strict preference relation and an indifference relation is unique. However, in fuzzy set theory, the intersection and the union of fuzzy sets can be represented different ways. Furthermore, some equivalent properties in the ordinary case have generalizations in the fuzzy framework that may be not equivalent. For these reasons there exist in the literature several factorizations of a fuzzy weak preference relation. In this paper we obtain and characterize different factorizations of fuzzy weak preference relations by means of two courses of action which are equivalent in the ordinary framework: axioms and definitions of strict preference and indifference.This work is partially financed by the Junta de Castilla y León (Consejería de Educación y Cultura, Proyecto VA057/02), Ministerio de Ciencia y Tecnología, Plan Nacional de Investigación, Desarrollo e Innovación Tecnológica (I+D+I) (Proyecto BEC2001-2253) and ERDF. I am indebted to José Luis García-Lapresta and an anonymous referee for his helpful comments.